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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 160080bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160080.l1 | 160080bx1 | \([0, -1, 0, -5976, -175824]\) | \(5763259856089/450225\) | \(1844121600\) | \([2]\) | \(110592\) | \(0.82518\) | \(\Gamma_0(N)\)-optimal |
| 160080.l2 | 160080bx2 | \([0, -1, 0, -5576, -200784]\) | \(-4681768588489/1621620405\) | \(-6642157178880\) | \([2]\) | \(221184\) | \(1.1717\) |
Rank
sage: E.rank()
The elliptic curves in class 160080bx have rank \(0\).
Complex multiplication
The elliptic curves in class 160080bx do not have complex multiplication.Modular form 160080.2.a.bx
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
